You must select 1 monster you control when you activate this card.
Sending the targeted monster to the Graveyard is part of this card's effect. If that monster is removed from the field by an effect chained to "Ruthless Denial", the effect to discard 1 card from your opponent's hand will not be applied.
If an effect chained to "Ruthless Denial" reduces the cards in your opponent's hand to 0, "Ruthless Denial's" effect cannot be applied, so you do not send the targeted monster to the Graveyard.
Both cards are considered to be sent to the Graveyard simulataneously.